G.H. PATEL COLLEGE OF ENGINEERING AND TECHNOLOGY

CHEMICAL ENGINEERING THERMODYNAMICS (2150503)

Topics : Lewis –Randall Rule ,excess properties ,excess Gibbs Energy & Activity coefficient , Nature of excess property

BY : JANKI PATEL (140110105033)• JAY PATEL (140110105034)• KEVIN PATEL (140110105035)• MIHIR PATEL (140110105037)

GUIDED BY : PROF. VIVAKSHA PATEL

CONTENT

•Lewis –Randall Rule•Excess properties & its nature •Gibbs excess Energy•Activity Coefficient

LEWIS –RANDALL RULE

• The Lewis-Randall rule is simply equation and fugacity of components in gas mixtures are evaluated .

• The Fugacity of solution can be determined by taking in to account deviation of actual solution from ideal behavior.

• As an ideal solution we can consider a gas mixture formed without any volume change on mixing the components. The volume of mixture is linear function of the mole number at a fixed temperature and pressure.

• Where is the molar volume of pure I at the same temperature and pressure.• For such ideal solutions ,

=() =• For pure components at a temperature T and pressure P ,

ln =()dp• After introducing above equation for the I component final equation becomes

ln = -)dp• We can also write it in the form of =

=• The above equation is commonly known as

as lewis-randall rule or lewis fugacity rule.

• It states that fugacity of component in an ideal solution is directly proportional to the mole fraction of the component in the solution.

EXCESS PROPERTIES

• The difference between the property of a real solution and an ideal solution is important in chemical thermodynamics and phase equilibria .

• The excess property is defined between an actual property and the property that would be calculated for same temperature , pressure, and composition by the equation for an ideal solution.

= M -

• M is the molar property of the solution and is the property of an ideal solution under the same conditions .

• The excess property change of mixing is defined in a similar manner.

∆ = ∆M - ∆ Above equation can also written in a form of ∆ = M - ∆ =

• ∆ =

• Above equation means that the excess property change of mixing and the excess property are the same.

• Excess function indicates the derivative from ideal solution behavior and easily related to the activity coefficients.

• Excess function may be positive or negative , when the excess Gibbs free energy of a solution is positive the solution is said to exhibit positive deviation from ideality.

• The definition of the partial molar excess function is analogous to that of partial molar thermodynamics properties.

• is the partial molar excess property of the component i. analogous to equation we can write ,

= Equation says that is the molar excess property of a solution is the average of partial molar excess property of each component weighed according to mole fraction .

EXCESS GIBBS FREE ENERGY

• For phase equilibrium studies the most useful excess property is the partial molar excess Gibbs free energy which can be directly related to the activity coefficient. Excess Gibbs free energy is defined as

• GE= G –Gid

• GE = ∑ xi ln

• Where is the excess chemical potential of component i.

= =

• the change in chemical potential fore component i. when it is transferred from its standard state to the solution at same temperature and pressure is related ato its fugacity in the solution .

= RT ln / =RT ln /

• Since fugacity in an ideal solution is can be written as =RT ln • In above equation the fugacityis related to , and as = so

equation becomes xi

= RT lnSo that molar excess Gibbs free energy of a solution is simply GE= RT ∑ xi ln xi

GE= G – (∑ xi Gi + RT ∑ xi ln xi )

ACTIVITY COEFFICIENT

An activity coefficient is a factor use in thermodynamics to account for deviations from ideal behaviour in a Mixture of chemical substances.

In an ideal mixture, the microscopic interactions between each pair of chemical species are the same (or macroscopically equivalent, the enthalpy change of solution and volume variation in mixing is zero) and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law.

• Deviations from ideality are accommodated by modifying the concentration by an activity coefficient.

Activity and concentration are related through the activity coefficient according to :

ai = ϓi . Mi

Activity coefficient different from unity arise because of the interaction of ions as concentration rises.

The degree of ion interaction depends on ionic charge as well as concentration.

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